How do you write an equation of a circle that contains (-2,-2), (2, -2) and (2,2)?

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Answer 1 · 2017-01-05T07:20:39

Equation of circle is $x^2+y^2=8$

Let the equation of the circle be $x^2+y^2+2gx+2fy+c=0$ .

As it passes through $(-2,2)$ , $(2,-2)$ and $(2,2)$ , putting their values, we get three equations as follows:

$(-2)^2+2^2+2g(-2)+2fxx2+c=0$ or $4+4-4g+4f+c=0$
or $-4g+4f+c=-8$ ...................................(1)

$2^2+(-2)^2+2gxx2+2f(-2)+c=0$ or $4+4+4g-4f+c=0$
or $4g-4f+c=-8$ ...................................(2)

$2^2+2^2+2gxx2+2fxx2+c=0$ or $4+4+4g+4f+c=0$
or $4g+4f+c=-8$ ...................................(3)

Adding (1) and (2) we get $2c=-16$ or $c=-8$ .

Subtracting (1) from (3) we get $8g=0$ or $g=0$ .

and putting these in (1), we get $0+4f-8=-8$ i.e. $f=0$

Hence equation is $x^2+y^2-8=0$ or $x^2+y^2=8$